+++ /dev/null
-// Copyright ©2017 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package gonum
-
-import (
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/lapack"
-)
-
-// Dgerqf computes an RQ factorization of the m×n matrix A,
-// A = R * Q.
-// On exit, if m <= n, the upper triangle of the subarray
-// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
-// If m >= n, the elements on and above the (m-n)-th subdiagonal
-// contain the m×n upper trapezoidal matrix R.
-// The remaining elements, with tau, represent the
-// orthogonal matrix Q as a product of min(m,n) elementary
-// reflectors.
-//
-// The matrix Q is represented as a product of elementary reflectors
-// Q = H_0 H_1 . . . H_{min(m,n)-1}.
-// Each H(i) has the form
-// H_i = I - tau_i * v * v^T
-// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
-// v[n-k+i:n] = 0 and v[n-k+i] = 1.
-//
-// tau must have length min(m,n), work must have length max(1, lwork),
-// and lwork must be -1 or at least max(1, m), otherwise Dgerqf will panic.
-// On exit, work[0] will contain the optimal length for work.
-//
-// Dgerqf is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
- checkMatrix(m, n, a, lda)
-
- if len(work) < max(1, lwork) {
- panic(shortWork)
- }
- if lwork != -1 && lwork < max(1, m) {
- panic(badWork)
- }
-
- k := min(m, n)
- if len(tau) != k {
- panic(badTau)
- }
-
- var nb, lwkopt int
- if k == 0 {
- lwkopt = 1
- } else {
- nb = impl.Ilaenv(1, "DGERQF", " ", m, n, -1, -1)
- lwkopt = m * nb
- }
- work[0] = float64(lwkopt)
-
- if lwork == -1 {
- return
- }
-
- // Return quickly if possible.
- if k == 0 {
- return
- }
-
- nbmin := 2
- nx := 1
- iws := m
- var ldwork int
- if 1 < nb && nb < k {
- // Determine when to cross over from blocked to unblocked code.
- nx = max(0, impl.Ilaenv(3, "DGERQF", " ", m, n, -1, -1))
- if nx < k {
- // Determine whether workspace is large enough for blocked code.
- iws = m * nb
- if lwork < iws {
- // Not enough workspace to use optimal nb. Reduce
- // nb and determine the minimum value of nb.
- nb = lwork / m
- nbmin = max(2, impl.Ilaenv(2, "DGERQF", " ", m, n, -1, -1))
- }
- ldwork = nb
- }
- }
-
- var mu, nu int
- if nbmin <= nb && nb < k && nx < k {
- // Use blocked code initially.
- // The last kk rows are handled by the block method.
- ki := ((k - nx - 1) / nb) * nb
- kk := min(k, ki+nb)
-
- var i int
- for i = k - kk + ki; i >= k-kk; i -= nb {
- ib := min(k-i, nb)
-
- // Compute the RQ factorization of the current block
- // A[m-k+i:m-k+i+ib-1, 0:n-k+i+ib-1].
- impl.Dgerq2(ib, n-k+i+ib, a[(m-k+i)*lda:], lda, tau[i:], work)
- if m-k+i > 0 {
- // Form the triangular factor of the block reflector
- // H = H_{i+ib-1} . . . H_{i+1} H_i.
- impl.Dlarft(lapack.Backward, lapack.RowWise,
- n-k+i+ib, ib, a[(m-k+i)*lda:], lda, tau[i:],
- work, ldwork)
-
- // Apply H to A[0:m-k+i-1, 0:n-k+i+ib-1] from the right.
- impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Backward, lapack.RowWise,
- m-k+i, n-k+i+ib, ib, a[(m-k+i)*lda:], lda,
- work, ldwork,
- a, lda,
- work[ib*ldwork:], ldwork)
- }
- }
- mu = m - k + i + nb
- nu = n - k + i + nb
- } else {
- mu = m
- nu = n
- }
-
- // Use unblocked code to factor the last or only block.
- if mu > 0 && nu > 0 {
- impl.Dgerq2(mu, nu, a, lda, tau, work)
- }
- work[0] = float64(iws)
-}
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